Which, no one is disputing. Invariant angular momentum in 3D Euclidean space can be specified with one coordinate along the z-axis; angular momentum in 4D Euclidean space needs to be defined by two coordinates corresponding to orthogonal planes that intersect at a point.

And please stop dropping the word Euclidean. If your OP is any indication of where you want to take, the fact that there's still only three Euclidean dimensions (the usual three dimensional space we all know and maybe love) in any hypothetical model of physics means that anything discussed in this thread is irrelevant to the real-world.

I told him that too. Didn't help.

(18-09-2015 12:23 PM)ZoraPrime Wrote: And you've delayed answering this question: what the fuck is the point of this thread anyway?

It's a spin-off from his trying to force quantum mechanics back into the classical box, because God.

Which, no one is disputing. Invariant angular momentum in 3D Euclidean space can be specified with one coordinate along the z-axis; angular momentum in 4D Euclidean space needs to be defined by two coordinates corresponding to orthogonal planes that intersect at a point.

And please stop dropping the word Euclidean. If your OP is any indication of where you want to take, the fact that there's still only three Euclidean dimensions (the usual three dimensional space we all know and maybe love) in any hypothetical model of physics means that anything discussed in this thread is irrelevant to the real-world.

Quote:The only place I have read anything to indicate that in 4D space a dust cloud would collapse into disc is here. Sorry if I am little skeptical....for all I know your just some internet crackpot.

And this is where your posts go to shit.

Because I honestly think you're getting confused over the word "disc," I will call the 4D Euclidean equivalent that's confined to two planes (instead of one plane/about one axis) a hyperdisk to avoid ambiguity.

The reason why a dust could collapses into a 3D Euclidean disc is because angular momentum is conserved. Similarly, the dust in 4D Euclidean space will still collapse into a hyperdisk because angular momentum is still conserved.

The conservation of angular momentum, like the other two conservation laws (energy and linear momentum), can be derived through Noether's Theorem. In short, if a system's Lagrangian (or more precisely, action) is invariant about a rotation, then angular momentum is conserved. I will take time explaining this, since I think you're not clear what needs to be invariant under rotations.

For angular momentum to be conserved, the system's Lagrangian that needs to be invariant under rotations. The Lagrangian is defined to be Kinetic Energy minus Potential Energy. To say that the Lagrangian is invariant under rotations mean that the kinetic energy term and potential energy time do not change under rotations. This isn't a difficult procedure to do, since for a gravitational potential, both kinetic energy and potential energy are determined by vector norms. I.e., kinetic energy is one-half times the mass times the vector norm squared of velocity; potential energy is (the sum of) constant times some masses over the norm of distance. Rotations, by construction, are designed to keep norms unchanged. So the Lagrangian is unchanged by rotations.

This may sound confusing, because doesn't the angular momentum conservation "bias" a system along a particular direction? Yes, it biases the system along a particular direction but not the Lagrangian. The reason is because the angular momentum the system has for all times is determined by the initial conditions. Two systems can have the same exact Lagrangian but two completely different initial conditions.

Therefore, a system in 4D Euclidean still will collapse into a hyperdisc by angular momentum conservation.

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And you've delayed answering this question: what the fuck is the point of this thread anyway?

Don't Live each day like it's your last. Live each day like you have 541 days after that one where every choice you make will have lasting implications to you and the world around you. ~ Tim Minchin

Quote:One notable feature, related to the number of simple bivectors and so rotation planes, is that in odd dimensions every rotation has a fixed axis – it is misleading to call it an axis of rotation as in higher dimensions rotations are taking place in multiple planes orthogonal to it. This is related to bivectors, as bivectors in odd dimensions decompose into the same number of bivectors as the even dimension below, so have the same number of planes, but one extra dimension. As each plane generates rotations in two dimensions in odd dimensions there must be one dimension, that is an axis, that is not being rotated.

In 3D space there is one dimension that is not being rotated....hence clouds can collapse into discs. In 4D space all dimensions are being rotated and no disc would form. You and ZoraPrime are simply mistaken.

You have got to be kidding me. If you think you understand it better then they do, then do the derivation and show it or STFU.

Also, don't mistake my poking fun at you as me not understanding the topic. I studied quantum mechanics in depth in graduate school. Spending quite some time on how EPR and NMR spectroscopy work which deal specifically with spin so we looked at spin quite in depth. I am just not going to waste my time answering you when you have already had your answer, one in terms simplified for you and one that was likely over your head. And you even have the balls to tell them that they are wrong when your responses indicate that you didn't even understand the question. They were quite good answers I might add.

"If we are honest—and scientists have to be—we must admit that religion is a jumble of false assertions, with no basis in reality.
The very idea of God is a product of the human imagination."
- Paul Dirac

(18-09-2015 11:43 AM)cjlr Wrote: You wouldn't get a disk - if by 'disk' you mean 2D entity in 3D space - because no shit you wouldn't. This is literally and explicitly what ZoraPrime said to you, which is why I said you didn't understand him:

(17-09-2015 09:58 AM)ZoraPrime Wrote: It's occurred to me that I think you're getting concerned over the word "disk." Yes, a 4D Euclidean "disk' (in the sense of how we're using it) spans over two planes. However, there's no word for "flat object that confines itself to particular plane(s)." We'd call them disks, even if they span two planes. It's like becoming concerned because someone uses the word "spherical symmetry" when discussing 4D Euclidean space and insisting "it's not a sphere, it's a hypersphere, so we should call it hypersherical symmetry." I'm calling it an accretion disk, even if it spans two planes, because I don't see why the fact it spans over two planes instead of one plane matters when it's orientation in space (i.e. the 4D angular momentum bivector) doesn't change.

I didn't see that part of ZoraPrime's post. I believe he edited in later after I originally read his post.

I am glad you are finally conceding that in a 4D space a dust cloud would not collapse into a disc.

(18-09-2015 12:50 PM)The Organic Chemist Wrote: You have got to be kidding me. If you think you understand it better then they do, then do the derivation and show it or STFU.

Also, don't mistake my poking fun at you as me not understanding the topic. I studied quantum mechanics in depth in graduate school. Spending quite some time on how EPR and NMR spectroscopy work which deal specifically with spin so we looked at spin quite in depth. I am just not going to waste my time answering you when you have already had your answer, one in terms simplified for you and one that was likely over your head. And you even have the balls to tell them that they are wrong when your responses indicate that you didn't even understand the question. They were quite good answers I might add.

The nice thing about the internet is you don't have to take the word of someone who claims to be an expert. You can spend a few minutes and do some research on your own to see if what they are claiming makes sense.

Here is how the conversation went:

Heywood: "Cjlr, I have a question for you, would a 4d electron have two spins?"Cjlr: "no"Heywood: "Oh...I thought it would because a 4d dust cloud has two spins and would not collapse into a disc....I know electron spin is not the same as classical spin"Organic Chemist: "The Yellow one....is the Sun!"Heyood to OC: "Get lost Copernicus"Cjlr in a condescending tone: "What makes you think that?"Heywood: "In 4D you would have spin in the XY plane and spin in the WZ plane"Cjlr: "Well you are wrong, spin occurs around a single axis...that is what spin is"ZoraPrime: "A 4d dust cloud would collapse into a hyperdisc"
.
.Cjlr: "Well obviously a 4d dust cloud wouldn't collapse into disc"

(18-09-2015 02:28 PM)Heywood Jahblome Wrote: The nice thing about the internet is you don't have to take the word of someone who claims to be an expert. You can spend a few minutes and do some research on your own to see if what they are claiming makes sense.

Actually, an expert understanding rather requires more than "a few minutes of your own research" to be able to speak to as an equal.

I leave it as an exercise to the reader to see where this might apply to the thread itself.

(18-09-2015 02:28 PM)Heywood Jahblome Wrote: Heywood: "In 4D you would have spin in the XY plane and spin in the WZ plane"
Cjlr: "Well you are wrong, spin occurs around a single axis...that is what spin is"
ZoraPrime: "A 4d dust cloud would collapse into a hyperdisc"
.
.
Cjlr: "Well obviously a 4d dust cloud wouldn't collapse into disc"

You still don't understand the difference between spin and angular momentum, nor the difference between quantum objects and classical mechanics.

So no, even though I admit to an overly broad phrasing - in the hope of getting through to you, since your "understanding" is entirely predicated on sloppy and inadequate analogies to intuitive classical behaviour! - I do not agree that any contradiction was given.

(18-09-2015 12:50 PM)The Organic Chemist Wrote: You have got to be kidding me. If you think you understand it better then they do, then do the derivation and show it or STFU.

Also, don't mistake my poking fun at you as me not understanding the topic. I studied quantum mechanics in depth in graduate school. Spending quite some time on how EPR and NMR spectroscopy work which deal specifically with spin so we looked at spin quite in depth. I am just not going to waste my time answering you when you have already had your answer, one in terms simplified for you and one that was likely over your head. And you even have the balls to tell them that they are wrong when your responses indicate that you didn't even understand the question. They were quite good answers I might add.

The nice thing about the internet is you don't have to take the word of someone who claims to be an expert. You can spend a few minutes and do some research on your own to see if what they are claiming makes sense.

Here is how the conversation went:

Heywood: "Cjlr, I have a question for you, would a 4d electron have two spins?"Cjlr: "no"Heywood: "Oh...I thought it would because a 4d dust cloud has two spins and would not collapse into a disc....I know electron spin is not the same as classical spin"Organic Chemist: "The Yellow one....is the Sun!"Heyood to OC: "Get lost Copernicus"Cjlr in a condescending tone: "What makes you think that?"Heywood: "In 4D you would have spin in the XY plane and spin in the WZ plane"Cjlr: "Well you are wrong, spin occurs around a single axis...that is what spin is"ZoraPrime: "A 4d dust cloud would collapse into a hyperdisc"
.
.Cjlr: "Well obviously a 4d dust cloud wouldn't collapse into disc"

Never said I was an expert, reread any post. I merely said that I studied it in depth. Cjlr is though and Zora seems to understand it as well. You are saying that your internet education is better than an academic one. Wikipedia is helpful but laughable as a concrete reference.

I will repeat what I said: show mathematically that they are mistaken or STFU. Or show the math and still STFU.

"If we are honest—and scientists have to be—we must admit that religion is a jumble of false assertions, with no basis in reality.
The very idea of God is a product of the human imagination."
- Paul Dirac

(18-09-2015 02:21 PM)cjlr Wrote: You never actually directly responded to him, but in any case, the changes were made over twelve hours prior to your posts today. It, of course, changes nothing either he or I said.

I don't always re-read a post after I have read it. Here is a direct question for ZoraPrime.

ZoraPrime. Cjlr made this claim, "the electron quite literally cannot have simultaneously well-defined spin in multiple axes". We all agree that in 3d space an object cannot have simultaneously well-defined spin in multiple axes". In 4d space can an object have well defined spin in multiple axes?